1. Feral/Guardian Druids, Cat and Bear forms get boring fast. They'd be the most boring class if Resto/Balance didn't save them. The only class/spec combo that I think truly makes me not want to play them because of the boring visuals.
2. All Rogues, odd on this list though because they SHOULD be the most bland. Theoretically you should never see them, not for long at least.
3. All Warriors only because Their armor tends to be flashier. Overall I think they look fine though some of their moves could be made a little more apparent for 3rd person view purposes.
4. Hunters. Marks/BM are the blandest, Survival has some pyro. Traps mitigate some of the appearance blandness and makes it look pretty good overall. Like Rogues you really shouldn't see them much.
5. Everything else. While Dks would probably be in this spot, I think they generally are just as flashy as they need to be.

Rogues need to get some shadow effects going on when they attack. Hell shadow blades is just black mist around the fists. They should turn into shadow and get blades flying around them. (just for visual) . Before mop i would have said warriors but not they catch fire and leave fire behind every time they charge. Atleast my undead does front flips when it attacks sometimes.

Rogues for sure. While Warriors animations are also boring, they make up for this slightly by being able to wield giant, badass weapons and shields. Rogues primarily just use boring little daggers and while there are some cool dagger models, they go mostly unnoticed unless you actually look closely.

Hunter is not flashy when your projectiles are barely visible. Their only notable animation is beastial wrath, which is BM-only.

Rogue is a close second, though. But at least for them it fits the idea of being stealthy.

"Oh, who does my hair? You might have heard of my stylist. It's called the Void!"
"No matter how much you plead I will not sprout tentacles or turn into a giant eyeball. Well, I might. But not because you asked!"

Shadow priest. Apart from Flay and sear, all our attacks are invisible, because they don't have a projectile.

agree. plus arcane mages with invisible nuke aka arcane blast. as far as locks, i know they used to have red skull appear over target for agony, but havent played mine in awhile so i dont know if that spell effect is still current. imo more spell effects in general would be nice, either via a projectile or a visible debuff on the target...i.e., destro lock casting immolate on target which is covered in flames.

Shadow priest. Apart from Flay and sear, all our attacks are invisible, because they don't have a projectile.

I was hoping someone would say this because I agree. A nearly invisible puff of cloud around the head of a target is hardly exciting. That's pretty much the entire story for Mind Spike, Mind Blast, Shadow Word: Pain, Vampiric Touch and Devouring Plague. I love shadow and have played it for years now but it's not because of the spell visuals.

I guess while I'm at it, I think that Smite could use a rework. Holy Fire is fine. Smite? eh....Don't know much about what the heals look like

Yeah... All in all, I'd have to say: Rogue is the blandest, most boring class in World of Warcraft.
Immediately followed up by the mage. Sure, it has some sparklies, but it's not very variable in looks, it's slow, and it's... Well, boring. Still, rogues take the cake. And vanish away with it.